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Preface | p. vii |
Random Polymer Models and their Applications | p. 1 |
Random Polymers and (De)Localization Phenomena | p. 1 |
A First Model: Pinning on a Defect Line | p. 6 |
Pinning a walk on a defect line | p. 6 |
Pinning more general processes on a defect line | p. 13 |
Entropic Repulsion and Wetting Phenomena | p. 17 |
Walls versus penetrable substrates | p. 20 |
The Denaturation Transition: Poland-Scheraga Models | p. 21 |
Force Induced Unzipping | p. 26 |
Inhomogeneous Charge Distributions: Copolymers and Pinning | p. 29 |
Periodic pinning models | p. 30 |
Copolymers, periodic copolymers and selective interfaces | p. 32 |
Copolymers with adsorption | p. 36 |
Fully Inhomogeneous Charge Distributions and Disordered Polymer Models | p. 37 |
Annealed models | p. 41 |
On the Return Time Viewpoint | p. 42 |
On Related Classes of Models | p. 43 |
More general return times | p. 43 |
Rewards and penalties on general structures | p. 45 |
Bibliographic Complements | p. 46 |
The Homogeneous Pinning Model | p. 49 |
The Free Energy | p. 49 |
Renewal Theory and Sharp Estimates | p. 52 |
Path Properties: The Infinite Volume Limit | p. 56 |
Path Properties: The Scaling Limit | p. 57 |
Bibliographic Complements | p. 63 |
Weakly Inhomogeneous Models | p. 69 |
A Formula for the Free Energy: Reduction to a Finite Dimension Problem | p. 69 |
Sharp Estimates on the Partition Function | p. 75 |
The Limit Path Trajectories | p. 77 |
The infinite volume limit | p. 78 |
The scaling limit | p. 80 |
First Order Transitions, Non-Uniqueness and Phase Diagrams | p. 82 |
Bibliographic Complements | p. 87 |
The Free Energy of Disordered Polymer Chains | p. 89 |
Preliminary Observations | p. 89 |
Existence of the Free Energy and Self-Averaging | p. 90 |
Periodic versus Disordered Charge Sequences | p. 94 |
Alternative Approaches to the Existence of the Free Energy | p. 96 |
Concentration inequalities and self-averaging | p. 96 |
The Super-Additive Ergodic Theorem approach | p. 97 |
Bibliographic Complements | p. 98 |
Disordered Pinning Models: The Phase Diagram | p. 101 |
Preliminary Observations on the Free Energy | p. 101 |
An Improved Lower Bound on the Free Energy | p. 102 |
On the Upper Bound: Annealing and Constrained Annealing | p. 109 |
The Effect of the Disorder on the Order of the Transition: A Smoothing Inequality | p. 111 |
What is One Expecting: The Renormalization Group Viewpoint and the Harris Criterion | p. 116 |
A Fully Inhomogeneous Non-Disordered Model | p. 118 |
Bibliographic Complements | p. 122 |
Disordered Copolymers and Selective Interfaces: The Phase Diagram | p. 127 |
Copolymers and Homogeneous Localization | p. 130 |
Rare Stretch Strategy for Localization Estimates | p. 135 |
The Weak Coupling Limit: Brownian Motion Model and Universality | p. 140 |
On more general copolymer models and the Brownian scaling | p. 142 |
Copolymers with adsorption | p. 144 |
Bibliographic Complements | p. 146 |
The Localized Phase of Disordered Polymers | p. 151 |
A First Tightness Estimate | p. 151 |
Quenched versus Quenched Averaged Estimates | p. 154 |
Quenched Averaged Estimates and the Infinite Volume Polymer Measure | p. 160 |
Bibliographic Complements | p. 164 |
The Delocalized Phase of Disordered Polymers | p. 167 |
Large Deviations and Delocalization | p. 168 |
Beyond Large Deviations: O(log N) Results | p. 170 |
The Strongly Delocalized Regime | p. 174 |
Bibliographic Complements | p. 177 |
Numerical Algorithms and Computations | p. 181 |
Computing the Partition Function | p. 182 |
Random walk models | p. 182 |
General renewal models | p. 183 |
The Fixman-Freire Algorithm | p. 184 |
A Statistical Test for Localization | p. 185 |
Applications: A Few Examples | p. 188 |
Bibliographic Complements | p. 191 |
Mathematical Tools | p. 193 |
Limit Theorems in Probability | p. 193 |
Some remarks on convexity | p. 196 |
Entropy | p. 196 |
Concentration Properties | p. 198 |
Slow Variation and Laplace Transforms | p. 200 |
Renewal Theory for N Valued Random Variables | p. 202 |
The renewal theorem | p. 204 |
The renewal mass function: Transient case | p. 206 |
The renewal mass function: Null recurrent case | p. 207 |
Scaling limits of renewal processes | p. 208 |
Random Walks | p. 212 |
The Super-Additive Ergodic Theorem | p. 214 |
Perron-Frobenius Theory | p. 216 |
Some Technical Estimates | p. 219 |
Homogeneous Localization Strategy: The Entropy Density | p. 219 |
The Weak Localization Limit | p. 221 |
Localization and Loss of Memory | p. 222 |
Effective Interface Models | p. 229 |
Ising Model, Effective Interface Models and Random Walks | p. 229 |
Bibliography | p. 233 |
Index | p. 241 |
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